Problem: Solve for $x$ and $y$ using elimination. ${-4x+3y = -18}$ ${-3x-3y = -45}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $3y$ and $-3y$ cancel out. $-7x = -63$ $\dfrac{-7x}{{-7}} = \dfrac{-63}{{-7}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-4x+3y = -18}\thinspace$ to find $y$ ${-4}{(9)}{ + 3y = -18}$ $-36+3y = -18$ $-36{+36} + 3y = -18{+36}$ $3y = 18$ $\dfrac{3y}{{3}} = \dfrac{18}{{3}}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {-3x-3y = -45}\thinspace$ and get the same answer for $y$ : ${-3}{(9)}{ - 3y = -45}$ ${y = 6}$